Triple articulation and the quadripod of a living system

In the last blog, we described how the variety of possible 1st order behavioral closures constituted superposed states representing all the possible behaviors able to be realized by a living system. This restricted the possible 3rd order behavioral closures that could be ‘chosen’ within the context of the circular closure of the system as a whole. This approach to the circular closure treats the formal 3rd order behavioral closure as sovereign over the efficient 2nd order closure. The diagonal superposition[1] relation in Figure 1 captures the dependency of the non-localised formal-cause decodings on the behaviors that can be realized by the localized material-cause encoding of the living system. Another approach, therefore, is to consider the formal superpositioning of possible behaviors as syntactical, constraining the possible efficient-cause semantics (Baez 1997) expressible in relation to a pragmatics of the relation of a living system to final cause (Boxer 2008).

Figure 1: superpositioned material states

This approach is better suited to giving an account of the efficient-cause behaviors of a living system, by which its genotypic behavioral strategy is described in its relation to its environment (Kineman 2018)[2] constrained by the effects in its environment induced by the reverse functors. These reverse functors were described in the previous blog. They define the entanglement[3] of the circular closure of the system with the circular causalities in its environment.

Figure 2: Environmentally-induced selection (einselection)

In terms of its behaviors, this relation of environmentally-induced selection (einselection[4]) not only situates the efficient-cause ‘choices’ within the context of the circular closure of the living system as a whole, but also entangled with the selective final-cause pressures in the environment with which it is structurally coupled. Efficient cause is thus subject both to the circular closure that defines the system identity and to this environmentally-induced selective pressure through entanglement. These selective pressures would be greatly intensified by the environment being a holobiont because of the nature of its circular closure of the systems structurally coupled with each of the four causes.[5]

Triple articulation and the quadripod of a living system

These two diagonal relations[6] provide a new perspective on the causally isolating ‘cut’ alongside the other two asymmetries defining a living system identity (Kineman 2008), described in the previous blog. Given that the living system is identified with its interaction with its environment being delayed temporally or separated spatially (Barandiaran, Di Paolo, and Rohde 2009), the superposition relation between formal and material causes is particularly identified with those aspects of causation that can be causally isolated from the larger system and its environment, described in terms of the state space of the living system that remain spatio-temporally isolated. In contrast the relation of einselection between efficient and final causes cannot be causally isolated, being particularly identified with the living system’s interactions with its environment.

The introduction of these two diagonal relations places the four causes in a relation to the three ‘cuts’ shown in Figure 3. Here the color of the arrows follow the previous blog: the blue arrows represent functor relations between the localized efficient and material causes and the non-localized final and formal causes. The orange arrows represent functor relations that cross over between the localized and non-localized causes, i.e., between the formal and efficient causes and between the material and final causes.

The circular causality of the system is further elaborated by the directedness of the edges in this quadripod, in which the ‘from’ end is dependent on the ‘to’ end. Each of its vertices has two ‘in’ relations and one ‘out’ relation (i.e., the formal and efficient causes) or vice versa (i.e., the material and final causes). The formal cause is thus dependent on what may be realized by both the efficient and material causes, while the efficient cause is dependent on both what may be realized by the material cause and by what ‘fits’ with the environment in relation to the final cause. In contrast, the material cause is only dependent on what ‘fits’ for the final cause, and the final cause is only dependent on what may be realized by the formal cause.


Figure 3: The quadripod spanning the three ‘cuts’

The relations of each cause to either side of the three ‘cuts’ are shown in Table 1, the ‘up’ and ‘down’ arrows used to indicate which sides of each ‘cut’ are implicit in each cause[7]:

Table 1: relating the four causes to the three ‘cuts’

The resultant quadripod, showing the relations between the four causes of a living system in Figure 4, is thus a way of describing the dynamics in how a living system takes up its being in relation to the three ‘cuts’ it makes as a triple articulation:


Figure 4: The quadripod structure of a living system

The different ways of viewing a living system

The view of a living system explored in the previous blog was based on the system having been causally isolated from its environment:

  1. The internalist view, in which the causally isolating relational ‘cut’ was held constant. Here the dependencies between the four causes, which define the system identity, are circular. This is the view used by evolutionary systems theory (Van de Vijver 1996), a view that describes the self-organizing holistic nature of biological living systems (Kineman and Wessman 2021).[8]

There are two other views of a living system, however, which emerge based on the other two ‘cuts’ being held constant:

  1. The externalist view, in which the ontic ‘cut’ defining the localized realities of the system’s interactions with its environment are held constant. Here the dependencies between the four causes go from the efficient cause to the material cause both directly and indirectly via the final and formal causes. This is the view used by Aristotle in establishing a physical theory of development, one based on a static nature of ‘nature’ itself (Van de Vijver 1998).[9]
  2. The architectural view, in which the epistemic ‘cut’ defining the relation between the localized and the non-localized is held constant. Here the dependencies between the four causes go from the formal to the final either via the efficient cause or via the material cause. This is the view that starts from a state-space definition of the interactions between a living system and its environment built up from category-theoretic ‘relational atoms’ (Kineman, Bánáthy, and Rosen 2007).[10]

Figure 5 shows how the four causes are arranged differently in each of these views together with the particular dependencies between the four causes in each case:


Figure 5: The three views of the quadripod

Each of these views provides insights into the domain of biological living systems while no one of them will capture all of what is going on with a living system in relation to its environment. Given each view’s way of holding one of the ‘cuts’ constant, note that while the internalist view captures the (self-organizing) circular causality of the living system, the architectural view shows the formal cause as being dependent on the final cause via the efficient and material causes, and the externalist view shows the efficient cause being dependent on the material cause both directly and via the final and formal causes. If we also examine the dependencies between the material, efficient and formal causes in terms of different orders of behavioral closure, then we see that the formal cause is only the ‘sovereign’ 3rd order behavioral closure in the internalist view, in the other two views it being a 2nd order behavioral closure describing superposed possible material behaviors. In the other two views, the relation of efficient cause to final cause is one of einselection. In the next blog, this different relation of the formal cause to the other causes will be reflected in the difference between an enterprise being driven from its center or from its edges.

Implications

In the next blog we will return to the doubling of the double task that becomes necessary in turbulent environments. I will explore how this quadripod can be applied to the way roles are understood within an enterprise that is understood as a living system[11]. This will attach particular importance to the architectural and externalist views in contrast to the internalist view explored in the previous blog. The final blog in this series will raise the issues of governance where adaptation has to become a general property of a system rather than one that remains external to it and address the implications of this for its supporting ecosystem.

This leaves the exploration of the human speaking being as a special case of a living system in which what is added is the relation of the living system as anoetic to noetic and autonoetic relations to its anoetic embodiment.[12]

Notes

[1] The closure of the material cause refers to the nodes in a graph representation that describe all the component parts of the material form, its edges describing their interactions and its closure meaning that there is at least one path to a node. The behavioral closure of this graph is then all the possible composite behaviors emerging from the behavioral interactions between these component parts from all possible starting states.  This behavioral closure is non-deterministic if the material cause can support more than one possible composite behavior from any given starting state. These possible alternative composite behaviors are superposed, a probabilistic description of their likely emergence taking the form of a density matrix.
[2] These genotypic behavioral strategies are (i) archaea-like replication – it “defends itself and benefits from self-preservation”; (ii) bacteria-like repair – it “reproduces and benefits from proliferation”; (iii) protobiota-like self-selection – it “serves a host and benefits from self-induced selection”; and (iv) eukaryote-like metabolism – it “builds capacity and benefits from innovative opportunity”. The quotes are from (Kineman 2018).
[3] There is an emergent body of thinking in terms of quantum biology (McFadden and Al-Khalili 2018; Cai 2016) that describes entanglement at the cellular level between an organism and its environment (Bordonaro and Ogryzko 2013), for example in carcinogenesis (Bordonaro 2019), in noncommunicable diseases (Bullon 2020), or in adaptive mutations (Ogryzko 1997, 2008).
[4] This environmentally-induced selection arising through the effects of entanglement (einselection) was originally formulated as a concept in terms of quantum physics, accounting for the emergence of classical states from superposed quantum states through decoherence processes (Zurek 1998; Castagnino, Laura, and Lombardi 2007; Zurek 2018).
[5] See the blog on ‘surrendering sovereignty‘. An introduction to holobionts as a concept is to be found in (Economist 2023). A holobiont is a way of thinking about agency at different levels of biological organization in ecosystems (Singh et al. 2013; Faure, Simon, and Heulin 2018). A human is better understood as a holobiont (van de Gutche, Blottiere, and Dore 2018), changing the way we can understand the role of the immune system (Schneider 2021): “… the holobiont’s boundaries and immunity are defined by the persistence of its complex system of interactions integrating existing and new interactions. This way of thinking presents a notion of immunity that materializes as the result of the complex interdependence relations between the different organisms composing the holobiont similar to that of an ecosystem”.
[6] This blog is not arguing that the diagonals are necessarily ‘explained’ by actually-existing dynamics between quantum states, which would be invoking a ‘realist’ interpretation of quantum theory (Oldofredi and López 2020).  Instead it is invoking a non-realist QBist way of understanding, in which Quantum Bayesianism provides a way of describing the probabilistic nature of our ability as observers to know either what behaviors are possible, expressed in terms of superposition, or what behaviors will be selected, expressed in terms of einselection (Fuchs 2010; Wallace 2020). This QBist approach is also applied to the methods of modeling associated with triple articulation, not to be confused with Relational Quantum Theory (Pienaar 2021).
[7] This sequence of the four causes here correspond to the ‘architectural’ view of the quadripod, described in the following section.  It is this view that was taken up in the stratification of cause in (Boxer 1998), referred to as follows: the why (final), the who-for-whom (efficient), the how (formal) and the what (material).
[8] This is the view corresponding to Kineman’s ‘identity closure’ and identified with an immune system’s role in conserving that identity closure (and therefore with the role of the Libidinal Economy of Discourses). It is the view elaborated by Guattari as identifying the characteristics of an assemblage of enunciation (Guattari 2013[1989]: p18):
“Schizoanalysis … could be the analysis of the impact of Assemblages of enunciation on semiotic and subjective productions in a given problematic context … what counts here is the idea of an existential circumscription that implies the deployment of intrinsic references – one might also say, a process of self-organization or singularization. Why this leitmotif of a return to Assemblages of enunciation? So as to avoid, as far as possible, getting bogged down in the concept of the ‘unconscious’.”
In Guattari’s work, the ontic ‘cut’ is about reference (exo/decoding x endo/encoding) and the epistemic ‘cut’ is about consistency (exo/non-localized x endo/localized).  Guattari goes on to identify the same quadripod structure in terms of “a graph that is representative of the Abstract machines populating the incorporeal Universes…” (Guattari 2013[1989]: p169). Guattari’s language is extraordinarily difficult to follow, but the structural parallels are striking.
[9] This is the view used to describe the way a business enterprise engages with its environment in terms of the relational forms of value proposition it offers to its customers   (Boxer 1998).
[10] This is the view taken by an enterprise architect in describing an organization as a socio-technical system (Miller and Rice 1967; Mostashari 2011; van de Wetering and Bos 2017). The epistemic ‘cut’ made by the organization institutes a ‘domain of relevance’ (Boxer 2014). This architectural view takes the form of a stratification in the relation of underlying technologies all the way through to end-users’ contexts-of-use.
[11] Other possible applications of the quadripod would be to the way we use language (Boxer 2018), to the drive structuration of object-relating (Boxer 1997), to the way these two quadripods are held in relation to each other in the structure of a discourse (Lacan 2007[1969-70]), to the dynamics of a social movement (Tupinambá 2021) and to economics (Karatani 2014).
[12] This introduces the Borromean RSI structures of Lacan and the relations to the Hegelian syllogisms that in Lacan’s work become the three moments and three crises (Boxer 2014c). Combining these RSI structures with the quadripod leads to the Lacanian discourses and to understanding the libidinal economy of discourses as operating like an immune system. To get to this, we will first have to understand the nature of the ‘turn’ in late Lacan’s work, a turn that will require us to separate out the thinking behind the Quadripod and the Borromean Knot in Lacan’s work.  This is something I have been unable to do until this series of blogs.  The first step along this path is to consider Zizek’s misreading of Lacan.

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